Question

The sum of three consecutive even numbers is 114. what is the smallest of the three numbers?​

Answer 1

Given :-

• Sum of three consecutive even numbers = 114

To Find :-

• The smallest number .

Solution :-

Let the three consecutive even numbers be x, x + 2 and x + 4 .

`\longrightarrow \rm x + x + 2 + x + 4 = 114`

`\longrightarrow \rm 3x + 6 = 114`

`\longrightarrow \rm 3x = 108`

`\longrightarrow \bf x = 36`

Smallest number = 36

Answer 2

36

Explanation:

Let's let n be any number.

If we multiply n by 2, we get 2n. Since anything multiplied by 2 is even, 2n must be even. Therefore, let 2n be our first number.

So, the consecutive even number will be (2n+2) followed by (2n+4).

We know that their sum must be 114. Therefore, we can write the following equation:

`(2n)+(2n+2)+(2n+4)=114`

Solve for n. Combine like terms on the left:

`6n+6=114`

Subtract 6 from both sides:

`6n=108`

Finally, divide both sides by 6. Therefore, the value of n is:

`n=108/6=18`

Therefore, our first even number is 2n or 2(18) which equates to 36.

And the consecutive even numbers will be 38 and 40.

So, the smallest of them, the first term, is 36.